1. Field of the Invention
Aspects of the invention relate to a method for linearizing energy spectra of radiation detectors for the measurement of one or more types of radiation, preferably X-ray, gamma, or nuclear particle radiation.
2. Description of the Related Art
Detector systems have a radiation detector for the measurement of one or more types of radiation and are well known in the prior art. One type of detector system which has a scintillation detector and a light detector. The response of scintillation detectors to gamma and other radiation is in general nonlinear. This means the appropriate signal amplitude per unit of energy (keV) at the output of the corresponding light detector, which may for example be a photomultiplier tube (PMT), a photodiode (PD), an avalanche photodiode (APD), a silicon drift detector (SDD) or a silicon photomultiplier, also known as Solid State Photomultiplier or Geiger mode APD array (SiPM), depends on the gamma energy. The signal amplitude or pulse height is usually expressed in a corresponding channel number of a pulse height spectrum.
The nonlinearities of the response of scintillation detectors are, among others, due to scintillator physics, and/or -nonlinear behavior of the photo detector. Nonlinearities (also called nonproportionalities, i.e. the conversion factor between the energy deposited in a scintillator and the number of visible photons produced is not constant) of the scintillators have been widely discussed in literature. An example of the literature is in W. W. Moses et al., IEEE Trans. Nucl. Sci. 55, 1049 (2008). They are intrinsic material properties and cannot be avoided.
Further, nonlinearities of photo detectors and/or associated electronics are often not only due to the detection principle and physics, but to imperfections of the detector chosen or due to the applied operating regime also. It might be necessary to accept those nonlinearities in order to compromise with other performance parameters (e.g. gain and noise contribution), in order to keep low the overall costs of detector systems, or because of a market not providing better detectors. Examples of such kind of nonlinearities are: Saturation effects of a photomultiplier tube (PMT) coupled to scintillators with high light output and short light decay time, which may occur at high gamma ray energies, as discussed in G. Pausch et al., IEEE Nucl. Sci. Symp. 2007, Conference Record, 963 (2007); and Saturation effects in a silicon photomultiplier (SiPM) which are due to the limited number of pixels, see e.g. Erik B. Johnson et al., IEEE Nucl. Sci. Symp. 2008, Conference Record, 1516 (2008).
Yet further, algorithms analyzing measured gamma ray spectra usually suppose a well known calibration of the energy scale. The algorithms for identifying radio-nuclides as used in many homeland security applications are relevant examples. If the response of the detector is nonlinear, the relation between channel number of the measured pulse height spectrum and absorbed gamma ray energy must be well known. This relation is called the calibration function.
The calibration function can be de-composed in a calibration factor, representing the relation between channel number and gamma energy for a fixed energy (e.g., 662 keV), and a linearization function describing the deviation from a linear scale.
Energy spectra measured with a certain calibration function can be re-binned to a spectrum with another calibration function. Re-binning means re-distributing the channel contents of an original spectrum to another spectrum with a changed scale by distributing the counts of all distinct channels in the (original) spectrum A to one or more channels in the (re-binned) spectrum A′ according to the overlap of original and transformed channels in the calibrated energy scale (exemplarily sketched in FIG. 1). Corresponding procedures or methods have been applied e.g. in handheld radio-nuclide identifiers.
In the state of the art, the calibration function (i.e. the calibration factor and the linearization function) are usually determined by—measuring gamma ray pulse height spectra of one or more radio nuclides providing photo peaks at known energies Ek; determining the positions of photo peaks in the pulse height spectra by common and well known peak fit algorithms applied to the measured peaks, which provide the corresponding channel numbers xk; and using the points (Ek, xk) as reference points (nodes) for the calibration function to be determined.
The nodes (Ek, xk) allow parameterization of the calibration function in accordance with the preferred approach (e.g. a polynomial of given grade) by least square fits or similar known procedures or methods.
This method has the disadvantage of working well only as long as a sufficient number of “good” photo peaks are available in the energy range of interest. In this context, a “good” photo peak means: the peak is well separated from other peaks, considering the actual detector resolution; the peak is due a single gamma (or X-ray) line, not due to group of lines with distances smaller than the detector resolution; and the peak is not noticeably distorted by background due to Compton scattering of more energetic gammas (X-rays) or other effects
A further disadvantage is that by applying the known peak fit algorithms, the accuracy of the fit depends on proper settings of the fit range and the fit conditions (like background subtraction method, mathematical form of the fit function). Therefore, the accuracy depends on the experience of the operator. It is therefore hard to obtain a stable quality of linearization in a production process with different operators.
Unfortunately, there are only a few common radionuclides generating “good” photo peaks in the energy region below 50 keV. “Common” radionuclides here mean nuclides which are commercially available and routinely applicable in a production process. This excludes nuclides which are too expensive, hard to access, hard to handle (e.g. gases and/or liquids) or distinguished by a short decay time which would require a frequent replacement of sources. On the other hand, this is just the energy region where the light output of all known scintillators considerably deviates from a linear behavior.
Using peaks which are not “good” has been the only practicable alternative for linearization of scintillation detectors in the energy range below 50 keV. Examples for such peaks are: the ˜32 keV peak due to Ba-kX rays emitted from Cs-137 sources—which is in fact composed of many components; and the ˜42 keV peak due to Sm-kX and Gd-kX rays from Eu-152 sources—which is in fact composed of many components.
A further disadvantage is that if common peak fit methods or procedures are applied to such “non good” photo peaks, the result is often deteriorated by systematic errors. This is because peak fit procedures suppose the shape of the peak to be fitted is identical with the shape of the fit curve. The linearization function determined in this way is therefore characterized by relatively large uncertainties in the energy range below 50 keV.
Yet a further disadvantage is that simultaneous multi-peak fitting procedures could be applied to “non good” photo peaks by experienced experts but are hard to adapt for a robust production process with non-expert operators.